function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices.
%
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));


m = size(X, 1);

% You need to return the following variables correctly
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m
%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the
%               first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%

yy = y;



X = [ones(m,1) X];
z2 = X * Theta1';
a2 = sigmoid(z2);
a2 = [ones(size(a2,1),1) a2];
z3 = a2 * Theta2';
h = sigmoid(z3);
j = yy .* log(h) + (1-yy) .* log(1-h);
J = -1/m * sum(sum(j));

regCost = lambda/2/m * ( sum(sum(Theta1(:,2:input_layer_size+1).^2)) + sum(sum(Theta2(:,2:hidden_layer_size+1) .^2)) );
J = J + regCost;





%%%%%%%%%%%%%%%%%%%%%%%%%

%output_error = h - y;
%hidden_error =  output_error * Theta2 .* [ones(m,1) sigmoidGradient(z2)];

%hidden_error = hidden_error(:,2:end);

%delta1 = hidden_error' * X;
%delta2 = output_error' * a2;

%Theta1_grad = 1/m * delta1;
%Theta2_grad = 1/m * delta2;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

delta1 = zeros(size(Theta1));
delta2 = zeros(size(Theta2));

for i = 1:m
y_3 = yy(i,:);
a_1 = X(i,:);
z_2 = a_1 * Theta1';
a_2 = sigmoid(z_2);
a_2 = [ones(size(a_2,1),1) a_2];
z_3 = a_2 * Theta2';
a_3 = sigmoid(z_3);
error3 = a_3 - y_3;
error2 =  error3 * Theta2 .* [1 sigmoidGradient(z_2)];
error2_trans = error2';
delta1 = delta1 + error2_trans(2:end,:) * a_1;
delta2 = delta2 + error3.' * a_2;
end

reg_1 = zeros(size(delta1));
reg_2 = zeros(size(delta2));
reg_1(:,2:end) = lambda/m * Theta1(:,2:end);
reg_2(:,2:end) = lambda/m * Theta2(:,2:end);
Theta1_grad = 1/m * delta1 + reg_1;
Theta2_grad = 1/m * delta2 + reg_2;

% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


end
